In many spectral devices characteristic radiation is generated by a small area of the sample surface. In such a case the source can be considered point like. In this case the conventional energy dispersive focusing technique is made either by cylindrical curved crystal (Advances in X-Ray Spectroscopy, Eds. C. Bonnelle, C. Mande, (Oxford, U.K., 1982)) or by doubly curved, on spherical or toroidal surfaces, crystal monochromators (U.S. Pat. No. 4,882,780; U.S. Pat. No. 4,807,268). These diffractors focus the monochromatic radiation onto the entrance detector slit. According to the Bragg's equation, the spectral resolution .DELTA..lambda./.lambda. depends both on .theta. and .DELTA..theta.: EQU .DELTA..lambda./.lambda.=.DELTA..theta./tan.theta. (1)
The intensity of the monochromatic radiation is proportional to the area of the diffractor surface, that reflects x-rays under the given Bragg's angle .theta. within the range .+-..DELTA..theta.. However, increasing the reflecting area, a widening of the aperture ratio of the diffractor occurs associated to a simultaneous decrease of the spectral resolution.
In the last decade analytical investigations of the shape and size of the reflecting area of a crystal-monochromator surface, employing different focusing methods have been carried out (D. B. Wittry and S. Sun, J. Appl. Phys. 67, 1633 (1990); D. B. Wittry and S. Sun, J. Appl. Phys. 68, 387 (1990); D. B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991); D. B. Wittry and S. Sun, J. Appl. Phys. 71, 564 (1992); W. Z. Chand and D. B. Wittry, J. Appl. Phys. 74, 2999 (1993)). Indeed, x-ray diffractors with double curved crystal provide significantly greater aperture ratio compared to that based on the cylindrical Johann or Johannson geometries. For such devices assuming an incidence angle .theta.&gt;20.degree. and a crystal height of L&lt;0.1R, the reflecting surface projection on the XZ plane is rectangular and the projection on the focal circle plane (XY plane) is an arc of radius R=2r, where r is the focal circle radius. The knowledge of the shape of the reflecting surface allows an estimation of the parameters of a spherical diffractor designed with a stepped surface (D. B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991)) and in the case of constant step height, the aperture of this diffractor is larger than a spherical curved crystal.